How do you remove the presence of an electromagnetic or gravitational field from a macroscopic or microscopic test environment, or rather how can you prove that the value of the charge or gravity is locally zero?

Let's take electromagnetism.  Any test on Earth or close by will be subject at the very least to the Earth's magnetic field.   If you create a shielded volume, how do you measure and prove there is no charge inside?  Must any device that measures electromagnetic field interact with the field itself and potentially change it?

Let's take gravity.  Any test involving mass-ive equipment will be subject to gravity.  Can you actually observe an absolute certain measurement for gravity, or only calculate it - is it subject to the uncertainty principle?

Is gravity quantum?  If the strength of a gravitational field is proportional to inverse square of distance between your measuring device and the object,  then is the value of the gravitational field really zero in some deepest parts of space where there is no mass anywhere within a distance that creates an excitation in the gravity field of 1q other than the device you are measuring with?

You can shield electromagnetic fields and reduce them to very, very small values. There are a number of experiments where this occurs, and some of them will describe how they test for those conditions. Parity non-conservation (PNC) experiments, for one.

In the atomic clocks I've built, we are convinced that the magnetic field is small by the fact that we can get our atoms to very cold (a few microKelvin) temperatures, which requires that the magnetic field be small. PNC and other ultra-precise experiments have even more stringent requirements.

You can get to a microgravity environment by going into free-fall, be it on a plane with a parabolic path, or on a body in orbit like the ISS.